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Resources tagged with Proof by contradiction similar to Approximations, Euclid's Algorithm & Continued Fractions:

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Challenge level:

Impossible Square?

Stage: 5 Challenge Level:

Can you make a square from these triangles?

An Introduction to Proof by Contradiction

Stage: 4 and 5

An introduction to proof by contradiction, a powerful method of mathematical proof.

Be Reasonable

Stage: 5 Challenge Level:

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.

Eyes Down

Stage: 5 Challenge Level:

The symbol [ ] means 'the integer part of'. Can the numbers [2x]; 2[x]; [x + 1/2] + [x - 1/2] ever be equal? Can they ever take three different values?

Rarity

Stage: 5 Challenge Level:

Show that it is rare for a ratio of ratios to be rational.

Rational Round

Stage: 5 Challenge Level:

Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.

Proof Sorter - the Square Root of 2 Is Irrational

Stage: 5 Challenge Level:

Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.

Staircase

Stage: 5 Challenge Level:

Solving the equation x^3 = 3 is easy but what about solving equations with a 'staircase' of powers?

Proximity

Stage: 4 Challenge Level:

We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

Tetra Inequalities

Stage: 5 Challenge Level:

Prove that in every tetrahedron there is a vertex such that the three edges meeting there have lengths which could be the sides of a triangle.